Temperatures in parts of Yorkshire an Lincolnshire are expected to reach 40C (107.6F).
East Midlands Railway warned of cancellations or reductions to its services from Sheffield and Lincoln.
The operator's Hull to Manchester Piccadilly route and Huddersfield to Leeds stopping service would also not run on Tuesday, it said. Several schools across Yorkshire and Lincolnshire have closed or are shutting early and many are relaxing their uniform policy to help pupils in the heatwave.Lincolnshire County Council said at 13:00 BST on Monday a road surface temperature of 54.3C was recorded in Martin, Timberland.Yorkshire Wildlife Park, near Doncaster, said it would remain closed on Tuesday to allow staff to look after the animals in the heat, although its Yorkshire Hive café and shop will open.
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